Highest Common Factor of 709, 940, 34 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 709, 940, 34 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 940, 34 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 709, 940, 34 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 709, 940, 34 is 1.
HCF(709, 940, 34) = 1
HCF of 709, 940, 34 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 709, 940, 34 is 1.
Highest Common Factor of 709,940,34 is 1
Step 1: Since 940 > 709, we apply the division lemma to 940 and 709, to get
940 = 709 x 1 + 231
Step 2: Since the reminder 709 ≠ 0, we apply division lemma to 231 and 709, to get
709 = 231 x 3 + 16
Step 3: We consider the new divisor 231 and the new remainder 16, and apply the division lemma to get
231 = 16 x 14 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 940 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(231,16) = HCF(709,231) = HCF(940,709) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34 > 1, we apply the division lemma to 34 and 1, to get
34 = 1 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 34 is 1
Notice that 1 = HCF(34,1) .
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Frequently Asked Questions on HCF of 709, 940, 34 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 709, 940, 34?
Answer: HCF of 709, 940, 34 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 940, 34 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 940, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.